CC MATH I STANDARDS UNIT 3 4.5 SOLVING TWO-STEP EQUATIONS: PART 1

WARM UP: Solve part (a) equations, and then use that to find part (b) answers.

1a) 94

94 −

=+ r

2a) 21

53=−x

3a) 511 −=+− u

1b) What is 3r?

2b) What is x – 2?

3b) What is u + 18?

4a) 543 =− s

5a) 67=

b

6a) 1432

=t

4b) What is 2s?

5b) What is 14−b ? 5b) What is 7

t?

INTRODUCTION TO SOLVING TWO-STEP STEP EQUATIONS:

Find numbers that answer the following questions: 1) What can you double and then add 5 to get 13? 2) What can you triple and then subtract by 7 to

get -1? 3) You can triple and then subtract by 1 to get 29?

4) What can you double and then add -6 to get -16? 5) What can you double and then subtract from 9

to get 5? 6) What can you half and then add 9 to get 15?

SOLVING TWO-STEP EQUATIONS: Verbal explanation by fill in the blanks

#1) 7m – 17 = 60 Step One: What minus 17 equals 60?

– 17 = 60 Step Two: What times 7 equals previous answer?

7 = #2) –2n – 25 = 13 Step One: What minus 25 equals 13?

– 25 = 13 Step Two: What times -2 equals previous answer?

-2 =

#3) 7 + 3x = 40 Step One: 7 plus what equals 40?

7 + = 40 Step Two: What times 3 equals previous answer?

3 =

#4) 12 + 5y = 27 Step One: 12 plus what equals 27?

12 + = 27 Step Two: What times 5 equals previous answer?

5 =

TWO-STEP EQUATIONS: Work Backwards

1) Find the VARIABLE. 2) Identify all operations. 3) In REVERSE ORDER of PEMDAS (SADMEP), cancel operations. 4) Use the same number and opposite operations

Operations: Operations: Operations: Operations: 1) 2y – 7 = 23 2) 8 + 6x = - 4 3) -5r - 18 = 12 4) 11 – 7x = 67

PRACTICE: SOLVING TWO-STEP EQUATIONS 1. 2127 =−x 2. 2447 =−a 3. 3774 =−x 4. 993 =−y 5. y9835 −= 6. 32128 =− x 7. 5.65.32 =−y 8. 75250 += x 9. )18(62 −+=x 10. 749 +=− m 11. 6122 =+g 12. 8528 −=− y

13. 1713 +=− h 14. 32713 −=+d 15. 5641 −=− x 16. 22310 =− x 17. 4727 =−y 18. 37512 =−− z 19. 2385 −=−n 20. r7325 +−= 21. 4026 =−x 22. 1443 =−y 23. 26)9(5 =−+x 24. )3(829 −+= y

CC MATH I STANDARDS: UNIT 3 4.5 SOLVING TWO-STEP EQUATIONS: PART 2

WARM UP: Solve for the given variable. 1) 1953 =−z

2) 6720 += y

3) 2149 −=+− x

4) 16311 =−− m

5) 7215 +−= x

6) r61032 +=−

SOLVING 2-STEP EQUATIONS WITH FRACTIONS • Solve in reverse order of operations = SADMEP • FRACTIONS represent DIVISION statements. • Be careful for hidden parentheses when there are OPERATIONS in numerator

Option #1: NO OPERATIONS IN NUMERATOR

Option #2: OPERATIONS IN NUMERATOR

453

=−n

435=

−n

PRACTICE PROBLEMS

1) 293

−=−b

2) 6915

−=−r

3) 1064

−=−−t

4) 5515

=+t

5) 6410

=−z

6) 729

=− p

7) 845

−=+y

8) 357=

+m 9) 9

215 −=− x

10) 634

−=−y

11) 534

=+−x

12) 17

12−=

− n

13) 32123

=+b

14) 62527

=− a

15) 5

732=

−s

WORD PROBLEMS INVOLVING MULTI-STEP EQUATIONS: Write an equation for the problem below and then solve the equation.

1) The product of negative 4 and y increased by 11 is equivalent to -5.

2) Eight more than five times a number is negative 62.

3) 8 less than twice a number is twelve.

4) The product of 5 and x decreased by 7 is as much as 42.

5) How old am I if 400 reduced by 2 times my age is 244?

6) For a field trip 4 students rode in cars and the rest filled nine buses. How many students were in each bus if 472 students were on the trip?

7) Sarah won 40 super bouncy balls playing

horseshoes at her school's game night. Later, she gave two to each of her friends. She only has 8 remaining. How many friends does she have?

8) You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost?

9) Two-thirds of a number minus six is –10

10) One-fourth of a number increased by 5 is as much as 3.

11) 3 fifths of a number less than 9 equals 2

12) 11 minus one-half of a number is -13.